You can take the log of the left and right hand side, and then apply the <span>logarithm rules:
log(a</span>ˣ) = x·log(a)
log(ab) = log(a) + log(b)
log(9^(x-1) * 2^(2x+2)) = log(6^(3x))
log(9^(x-1)) + log(2^(2x+2)) = 3x log(6)
(x-1) log(9) + (2x+2) log(2) - 3x log(6) = 0
x(log9 + 2log2 - 3log6) = log9 - 2log2
x = (log9 - 2log2) / (log9 + 2log2 - 3log6)
simplifying by writing log9 = 2log3 and log6 = log2+log3
x= 2(log3 - log2) / (2log3 + 2log2 - 3log2 - 3log3) =
x= -2(log3 - log2) / (log3 + log2) = -2 log(3/2) / log(6)
So 6^x = 4/9
The answer is c because if head appears and the spinner is spun with 1 - 4 on it then you can get either h1, h2, h3 or h4 and if tales appears and another coin is tossed you can get either th or tt
Answer:
a) 0.70
b) 0.82
Step-by-step explanation:
a)
Let M be the event that student get merit scholarship and A be the event that student get athletic scholarship.
P(M)=0.3
P(A)=0.6
P(M∩A)=0.08
P(not getting merit scholarships)=P(M')=?
P(not getting merit scholarships)=1-P(M)
P(not getting merit scholarships)=1-0.3
P(not getting merit scholarships)=0.7
The probability that student not get the merit scholarship is 70%.
b)
P(getting at least one of two scholarships)=P(M or A)=P(M∪A)
P(getting at least one of two scholarships)=P(M)+P(A)-P(M∩A)
P(getting at least one of two scholarships)=0.3+0.6-0.08
P(getting at least one of two scholarships)=0.9-0.08
P(getting at least one of two scholarships)=0.82
The probability that student gets at least one of two scholarships is 82%.
320 i believe... the original answer was 317.52
Answer:
x = 20
Step-by-step explanation:
these are vertical angles and vertical angles are congruent
3x+50 = 6x-10
3x = 6x - 60
-3x = -60
x = 20
